Answer the questions below with explanations

For the tenpin howling scores in Question 14.6: 13311 Score sum 5m ofsquares 1 113, 166, 119, 133, 199I 9011 162,616 2 195, 206, 133, 195, 210, 221 1,215 246,991 3 169, 155, 192, 133 634 11?,514 (i) Construct an ANOVA table to test the whether there is a difference between the performances of the three bowling balls. (ii) 'What assumption does your conclusion depend on? Example $22.1. {i} {ii} Four years ago a life then aged 35 eEected a 25year without prots endowment assurance by annual premiums for a sum assured of .Em payable at the end of the year of death or on sunrival for 25 years. He surrendered the policy just before paying the premium now due. The life ofce calculated the premiums for this policy on the basis of 111957711} select at 4% interest with the following expense loadings: 2.5% each premium, including the rst, plus a further initial expense of 1% of the sum assured. The ofce also calculates reserves on this basis, and surrender values are equal to 95% of reserves. {a} Calculate the oice annual premium. {b} Calculate the surrender value of the policy. Suppose that the policyholder of {i} had made his policy paidup instead of surrendering it, and that the ofce calculates paidup values by the proportionate rule. Calculate the yield per annum {to the nearest 13.1%} that he would have obtained on his entire transaction, assuming that he survives to maturity date